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1. Entanglement entropy from entanglement contour: higher dimensions

   https://doi.org/10.21468/SciPostPhysCore.5.2.020  

   Han, Muxin; Wen, Qiang (January 2022, SciPost Physics Core)

   We study the entanglement contour and partial entanglement entropy (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy is evaluated from a certain limit of the PEE with a geometric regulator. In the context of the entanglement contour, we classify the geometric regulators, study their difference from the UV regulators. Furthermore, for spherical regions in conformal field theories (CFTs) we find the exact relation between the UV and geometric cutoff, which clarifies some subtle points in the previous literature. We clarify a subtle point of the additive linear combination (ALC) proposal for PEE in higher dimensions. The subset entanglement entropies in the ALC proposal should all be evaluated as a limit of the PEE while excluding a fixed class of local-short-distance correlation. Unlike the 2-dimensional configurations, naively plugging the entanglement entropy calculated with a UV cutoff will spoil the validity of the ALC proposal. We derive the entanglement contour function for spherical regions, annuli and spherical shells in the vacuum state of general-dimensional CFTs on a hyperplane. 

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2. Verlinde formula from entanglement

   https://doi.org/10.1103/PhysRevResearch.2.023132  

   Shi, Bowen (May 2020, Physical Review Research)

   null (Ed.)
3. Fusion rules from entanglement

   https://doi.org/10.1016/j.aop.2020.168164  

   Shi, Bowen; Kato, Kohtaro; Kim, Isaac H. (July 2020, Annals of Physics)
4. Conformal geometry from entanglement

   https://doi.org/10.21468/SciPostPhys.18.3.102  

   Kim, Isaac H; Li, Xiang; Lin, Ting-Chun; McGreevy, John; Shi, Bowen (January 2025, SciPost Physics)

   In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities(\mathfrak{c}_{\textrm{tot}}, \eta) $({𝔠}_{\text{tot}},\eta )$that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i)\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii)\eta $\eta$is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is equivalent to a vector fixed-point equation involving\eta $\eta$, making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions. 

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5. Identifying primes from entanglement dynamics

   https://doi.org/10.1103/PhysRevA.108.042404  

   Southier, A. L. M.; Santos, Lea F.; Souto Ribeiro, P. H.; Ribeiro, A. D. (October 2023, Physical Review A)